All of the PC races in the PHB are available, however Elves and Gnomes are slightly altered.
Additional Player Character races: Kobold, Tabaxi.
Other races are subject to DM approval.
NOTE: Players should never feel constrained by the typecasting of demi-Human races, but they should be the exceptions to the general rule that NPC demi-Humans behave according to type. True diversity belongs to Humans.
Once again, Player Characters should never feel constrained to play to type, but NPCs will almost always conform to the types described.